LSU
Mathematics

Math 1022 Trigonometry Topics

An Introduction to Angles: Degree and Radian Measure

• Understanding degree measure and radian measure
• Converting between degree measure and radian measure
• Finding coterminal angles using degree measure and radian measure

Applications of Radian Measure

• Determining the area of a sector of a circle
• Determining the arc length of a sector of a circle

Triangles (Review)

• Classifying triangles
• Using the Pythagorean Theorem
• Understanding similar triangles
• Understanding the special right triangles

Right Triangle Trigonometry

• Understanding the right triangle definitions of the trigonometric functions
• Using the special right triangles
• Understanding the fundamental trigonometric identities
• Understanding cofunctions
• Evaluating trigonometric functions using a calculator

Trigonometric Functions of General Angles

• Understanding the four families of special angles
• Understanding the definitions of the trigonometric functions of general angles
• Finding the values of the trigonometric functions of quadrantal angles
• Understanding the signs of the trigonometric functions
• Determining reference angles
• Evaluating trigonometric functions ofangles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families

The Unit Circle

• Understanding the definition of the unit circle
• Understanding the unit circle definitions of the trigonometric functions

The Graphs of the Trigonometric Functions

• Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
• Sketching graphs of the form y=Asin(Bx-C)+D or y=Acos(Bx-C)+D
• Sketching graphs of the form y=Atan(Bx-C)+D or y=Acot(Bx-C)+D
• Sketching graphs of the form y=Asec(Bx-C)+D or y=Acsc(Bx-C)+D
• Determine the equation of a function of the form y=Asin(Bx-C) or y=Acos(Bx-C) given its graph

Inverse Trigonometric Functions

• Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
• Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$

Trigonometric Identities

• Substituting known identities to verify an identity
• Changing to sines and cosines to verify an identity
• Factoring to verify an identity
• Separating a single quotient into multiple quotients to verify an identity
• Combining fractional expressions to verify an identity
• Multiplying by conjugates to verify an identity

The Sum and Difference Formulas

• Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
• Using the sum and difference formulas to verify identities
• Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions

The Double-Angle and Half-Angle Formulas

• Understanding and using the double-angle formulas and the half-angle formulas
• Using the double-angle and half-angle formulas to verify identities
• Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions

Trigonometric Equations

• Solving trigonometric equations that are linear or quadratic in form
• Solving trigonometric equations using identities
• Solving other types of trigonometric equations
• Solving trigonometric equations using a calculator

Right Triangle Applications

• Solving right triangles
• Solving applications using right triangles

The Law of Sines

• Determining if the Law of Sines can be used to solve an oblique triangle
• Using the Law of Sines to solve the SAA case or the ASA case
• Using the Law of Sines to solve the SSA (Ambiguous) case
• Using the Law of Sines to solve applied problems involving oblique triangles

The Law of Cosines

• Determining if the Law of Cosines can be used to solve an oblique triangle
• Using the Law of Cosines to solve the SAS case
• Using the Law of Cosines to solve the SSS case
• Using the Law of Cosines to solve applied problems involving oblique triangles

Area of Triangles

• Determining the area of oblique triangles
• Using Heron’s Formula to determine the area of an SSS triangle
• Solving applied problems involving the area of triangles

Polar Coordinates and Polar Equations

• Plotting points using polar coordinates
• Determining different representations of a point (r, θ)
• Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
• Converting equations from rectangular to polarform and from polar to rectangular form

Graphing Polar Equations

• Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
• Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
• Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
• Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
• Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$

Vectors

• Understanding the geometric representation of a vector
• Understanding operations on vectors represented geometrically
• Understanding vectors in terms of components
• Understanding vectors in terms of i and j
• Finding a unit vector
• Determining the direction angle of a vector
• Representing a vector in terms of i and j given its magnitude and direction angle
• Using vectors to solve applied problems involving velocity